1. Field of the Invention
This invention relates generally to electronic oscillating circuits and more particularly to oscillators wherein fluctuation of frequency and amplitude of the oscillator is minimized with variation of temperature.
2. Description of Related Art
Oscillators and modulation of frequencies for Frequency Shift Keying (FSK) transmission of digital data signals is well known in the art. A review of a general form of the criteria for designing an oscillator circuit of the prior art is described in Modern Communication Circuits, Jack Smith, McGraw-Hill, 1986, New York, and shown in FIG. 1. The necessary components of an oscillator are a frequency dependent gain circuit 100, a frequency dependent feedback circuit 105, and a combining block 110. The output V.sub.o 120 of the gain circuit 100 is the input to the feedback circuit 105. The input signal V.sub.i 115 is combined with the output V.sub.fb 107 of the feedback circuit 105 to form the input 112 of the gain circuit 100.
The gain of the gain block 100 is designated G(j.omega.) and the gain of the feedback circuit 105 is designated H(j.omega.). These gains G(j.omega.) and H(j.omega.) describe the relationship of their respective output signals V.sub.o 120 and V.sub.fb 107 to their respective input signals 112 and V.sub.o 120. Therefore, the output signal V.sub.o 120 becomes ##EQU1## For an oscillator, the output signal V.sub.o 120 must be nonzero even if the input voltage V.sub.i 115 is zero. For this to be true, then EQU 1+G(j.omega.)H(j.omega.)=0 EQU or EQU G(j.omega.)H(j.omega.)=-1.
That is, the magnitude of the open-loop transfer function must be equal to 1 and the phase shift of the gain circuit 100 and the feedback circuit 106 must be 180.degree..
FIG. 2 shows a common base amplifier. There is fundamentally no phase shift between signals at the emitter and the collector of the transistor Q1 130. The feedback circuit is designed to meet the Nyquist criteria, where the amplitude of the input 135 of the feedback circuit 125 is equal to and out of phase from the amplitude of the output 140.
Theoretically, the transistor Q1 130 is ideal and has no frequency components. Therefore, the feedback circuit determines the single frequency of oscillation of the circuit.
FIG. 3a shows a basic oscillator circuit. The transistor Q1 300, capacitor C.sub.B 310, the base biasing resistor R.sub.B 305, and the emitter resistor R.sub.E 315 form the gain circuit 100. The input 120 of the feedback circuit 105 is at the collector of the transistor Q1 300. The feedback circuit 105 consists of the inductor L 330 in parallel with the series combination of the first capacitor C.sub.1 320 and the second capacitor C.sub.2 325. The output 107 of the feedback circuit 105 is connected to the emitter of the transistor Q1 300.
The base biasing resistor R.sub.B 305 provides a biasing current from the power supply voltage source V.sub.CC 335 to the base of the transistor Q1 300. The base capacitor C.sub.B 310 is sufficiently large that the impedance of the base capacitor C.sub.B 310 is very small at the frequency of interest thus forming the common base transistor of FIG. 2.
The voltage developed at the output 107 of the feedback circuit 105 is developed across the emitter resistor R.sub.E 315 creating the emitter current of the transistor Q1 300 which in turn creates the collector current of the transistor Q1 300. The load resistor R.sub.L 340 sinks the collector current to develop the output signal V.sub.o 120. The blocking capacitor C.sub.BLK 345 prevents any D.C. current from flowing through the load resistor R.sub.L 340.
FIG. 4a shows a simplified equivalent circuit of the oscillator of FIG. 3. The transistor Q1 300 is represented by the standard Hybrid .pi. model. For simplicity of calculation, the output resistance R.sub.o 410 and the impedance of the base charging capacitance C.sub.b 415 are ignored. This is because their magnitude is sufficiently small to have little effect on the oscillator design. The small signal input resistance r.sub..pi. 405 is given as: ##EQU2## where V.sub.be is the base-emitter voltage.
I.sub.c is the collector current. PA1 .beta..sub.o is the small signal current gain. PA1 g.sub.m is the transconductance of the transistor Q1 300. PA1 C is the series combination of the first capacitor C.sub.1 320 and the second capacitor C.sub.2 325 and determined as ##EQU8## PA1 C.sub.eff is the stray capacitor Cstray 420 of FIG. 4a in parallel with the series combination of the first capacitor C.sub.1 320 and the second capacitor C.sub.2 325 of FIG. 4a and is determined as ##EQU14## The temperature coefficient of the inductor L 330 of FIG. 4a is from approximately 25 ppm/.degree. C. to approximately 125 ppm/.degree. C. The first capacitor C.sub.1 320 and the second capacitor C.sub.2 325 of FIG. 4a each have a temperature coefficient of approximately 50 ppm/.degree. C. The capacitance of the stray capacitor Cstray 420 is not easily predicted or controlled and further has a higher temperature coefficient compared to that of the first capacitor C.sub.1 320 and the second capacitor C.sub.2 325 of FIG. 4a. To minimize the effect of the stray capacitor Cstray 420, the value of the first capacitor C.sub.1 320 and the second capacitor C.sub.2 325 are made larger. PA1 C.sub.1 is the first impedance, and PA1 C.sub.2 is the second impedance. PA1 C.sub.1 is the first capacitance, and PA1 C.sub.2 is the second capacitance.
The collector current I.sub.c is provided by the current source 400 and the current is determined by the function: EQU I.sub.c =g.sub.m V.sub.be
where
The requirements for oscillation as stated above are for the open loop gain of the combination of the gain circuit 100 and the feedback circuit 105 to be equal to 1 and the phase shift of the gain circuit 100 and the feedback circuit 105 to be 0.degree.. To examine the open loop gain of the oscillator of FIG. 3a refer now to FIG. 4b. It is well known, that the when the loop is opened, the impedances at each node should be equal to those of the dosed loop. Therefore, the input resistance r.sub.i 410 is determined as: ##EQU3## where ##EQU4## is the voltage equivalent of temperature.
It can be further shown by circuit analysis that the input resistance input resistance r.sub.i 410 and the emitter resistance R.sub.E 315 can be transformed to the equivalent resistor R.sub.eq 415 of FIG. 4c. The equivalent resistor R.sub.eq 415 is determined by the formula: ##EQU5## The voltage V is further determined as: ##EQU6##
From the above the forward loop gain G(j.omega.) of the gain circuit 100 is determined as: ##EQU7## where Z.sub.L is the impedance from the output node V.sub.o 120 to the ground reference point and is: EQU Z.sub.L.sup.-1 =(j.omega.L).sup.-1 +R.sub.eq.sup.-1 +R.sub.L.sup.-1 +(j.omega.C)
where
The feedback gain H(j.omega.) of the feedback circuit 105 is determined as: ##EQU9##
For the circuit to oscillate, the phase shift through the combination of the gain circuit 100 and the feedback circuit 105 is not dependent on frequency, the phase shift of the gain circuit 100 must be 0.degree.. Since the phase shift of the gain block 100 is not dependent on frequency, the phase shift of the feedback circuit 105 must be zero. This occurs at one frequency (.omega..sub.0). The frequency .omega..sub.0 is determined as: ##EQU10## At the frequency, the impedance Z.sub.L becomes: ##EQU11## and the open loop gain G(j.omega.)H(j.omega.) of the oscillator becomes: ##EQU12## The final condition for oscillation is that open loop gain G(j.omega.)H(j.omega.) equal to 1.
FIGS. 4d and 4e are gain and phase diagrams of the circuit of FIG. 4a showing the open loop gain and open loop phase of the circuit. As shown above, the circuit will oscillate naturally when the loop is closed at a frequency .omega..sub.0. This frequency is where the gain is maximum 425 and the phase shift is zero 430.
The fundamental frequency of oscillation f.sub.0 and the amplitude V.sub.O can be made to fluctuate or vary from their respective designed values by changes in temperature and the magnitude of parasitic or stray capacitance C.sub.stray 420.
In practical implementations, the inductor L 330 is modeled as shown in FIG. 4F. The resistor R.sub.s 440 represents the resistance inherent in the conductor used to form the inductor L 330. The inductor L 435 is the ideal inductance of the conductor and is a function of the cross-sectional area, the length, and the permeability of the surrounding environment.
The cross-sectional area and the length of the conductor that forms the inductor L 330 changes with temperature. These changes thus change the value of the ideal inductor L 435. The changes of the value of the ideal inductor L 435 are difficult to predict and are best characterized by measurement.
The capacitor C.sub.P 445 is the distributed capacitance between each winding of the inductor L 330. Generally, this capacitance is considered a contributor to the stray capacitance C.sub.stray 420 of FIG. 4c, but has a negligible effect on the value of the stray capacitance C.sub.stray 420 of FIG. 4c.
The capacitor C.sub.stray 420 of FIG. 4c, in addition to the interwinding capacitance of the inductor L 330, also consists of the output capacitance of the transistor Q1 300, the capacitance of the interconnection traces on the semiconductor die from the collector of the transistor Q1 300, the wirebonds from the semiconductor die to the lead frame, and the wiring traces of printed circuit board connecting the components of the oscillator. The capacitor C.sub.stray 420 is in parallel with the series combination of the first and second capacitors C.sub.1 320 and C.sub.2 325 and will change the natural frequency of oscillation .omega..sub.0 of the oscillator. The output capacitance of the transistor Q1 300 is particularly sensitive to changes in temperature and provide the greatest sensitivity of the capacitor C.sub.stray 420 to temperature.
The input resistor R.sub..pi. 405 of the transistor Q1 300 of FIG. 4a, the emitter resistor R.sub.E 315, the series resistance R.sub.S 440 of the inductor L 330 and the load resistance R.sub.L 340 determine the amplitude of the of the output signal. Each of these resistances will vary according to their independent temperature coefficients (TC). The temperature coefficient indicate the amount of variance each resistance changes with a change in temperature. These changes with temperature will thus change the amplitude of the voltage developed across the load resistance R.sub.L 340.
FIG. 3b illustrates a common base transistor oscillator in which the base capacitance C.sub.B 310 is replaced with a surface acoustic wave resonator (SAWR) 350. In this instance, the gain block 100 now has the frequency response of the SAWR 350 as a determinant of the natural frequency of oscillation. FIGS. 5a and 5b show respectively the gain and phase of the common base transistor oscillator of FIG. 3b. The open loop gain of the common base transistor oscillator of FIG. 3b has a peak 500 when the phase 505 is 0.degree. indicating the frequency f.sub.o of oscillation. This is the point of serial resonance f.sub.s of the SAWR 350 of FIG. 3b. There are two other points with a 0.degree. phase shift 510 and 515. These are the point of parallel resonance f.sub.p of the SAWR 350 of FIG. 3b and the point of resonance f.sub.o of the feed back circuit 105. The gain at these two points 510 and 515 is not sufficient to sustain oscillation.
FIGS. 6a and 6b illustrate the effect of temperature on the frequency of oscillation of the common base transistor oscillator of FIGS. 3a and 3b. FIG. 6a shows the plots of the open loop phase shift of the common base transistor oscillator of FIG. 3a at the temperatures of 40.degree. C., +25.degree. C., and +80.degree. C. As can be seen, the frequency of oscillation drifts from the point 520 at -40.degree. C. to the point 525 at +25.degree. C., to the point 530 at +80.degree. C. It is well known in the art that the frequency of oscillation f.sub.o is found by the function: ##EQU13## where: L is the inductor L 330 of FIG. 4a.
FIG. 6b shows the open loop phase of the common base transistor oscillator of FIG. 3b employing the SAWR 350. The frequency of resonance of the SAWR is relatively insensitive to temperature. However, in combination with components of the feedback circuit 105, the open loop phase of the common base transistor oscillator is a combination of the phase shift of the feedback circuit 105 and the SAWR 350. Consequently, the temperature effects show that the common base transistor oscillator of FIG. 3b has a 0.degree. phase at the natural frequency 520 of the feedback circuit 105 for a temperature of -40.degree. C. On the other hand, the open loop phase of the common base transistor oscillator of FIG. 3b may marginally reach 0.degree. phase shift at the frequency 540 of the SAWR 350 for a temperature of +80.degree. C. The only predictable frequency of oscillation 505 is at 25.degree. C. The above indicates that the frequency of the common base transistor oscillator can not be well controlled over large changes in temperature. This instability of frequency limits the application of the common base transistor oscillator in applications having environments with extreme changes in temperature such as Radio Frequency Identification (RFID) and telemetry.
U.S. Pat. No. 5,367,537 (Anderson) describes a transmitter having improved noise immunity characteristics relative to Amplitude Shift Keying methods currently utilized in the art and a wide deviation in frequency between a first and second transmission frequency corresponding to binary data transmission in FSK modulating transmitter. Anderson describes a low-power requirement FSK modulating circuit, which has an oscillation amplifier tuned for RF oscillation and responsive to oscillatory input thereto. A Surface Acoustic Wave (SAW) transducer having a natural resonant frequency in a stand alone oscillatory configuration provides a frequency for the FSK modulating circuit. A single reactive component located between the SAW transducer and the RF oscillator amplifier provides a pulling effect upon the SAW natural resonant frequency so to change the oscillatory frequency input to the RF oscillator amplifier to a second frequency. A PIN switching diode in parallel with the reactive component provides a bypass of that reactive component such that the SAW transducer provides its natural resonant frequency as an input to the RF oscillator amplifier. Means for forward and reverse biasing the PIN diode provide selective control over these two independent frequencies.
U.S. Pat. No. 5,532,654 (leki et al.) describes an FSK modulator. The FSK modulator has an amplifier for oscillation, a SAW resonator connected in series with a switching circuit containing one or more fixed capacitors. The capacitors are switched in series with the SAW resonator to switch the frequency of oscillation of the modulator according to a signal at the input of the switching circuit.
U.S. Pat. No. 5,168,251 (Zennano, Jr. et al.) is based on the recognition that the Q of a tuned filter can be improved, while minimizing the overall size of the filter to within restricted cavity size limitations, by respectively replacing single inductors and capacitors in conventional filter structures with parallel multiple inductors and/or multiple series capacitors as required. More specifically, Zennano, Jr. et al. describes a tuned filter is provided that includes an input terminal and an output terminal; a first network coupled to the input terminal and electrical ground including a plurality of series capacitors and/or a plurality of parallel inductors; and a second network coupled to the input terminal and the output terminal including at least one of a plurality of series capacitors and/or a plurality of parallel inductors. The quality factor (Q) of the filter is improved by the use of the series capacitors and/or parallel inductors as opposed to single capacitors or inductors.
U.S. Pat. No. 5,793,261 Bolling, III) describes a digitally controlled SAW stabilized FSK oscillator circuit having an oscillator and a single-port SAWR with a pre determined circuit resonant frequency and being coupled to the oscillator for establishing a first oscillator output frequency. F.sub.SAW. A bipolar transistor has at least one predetermined shunt capacitance value C that is placed in electrical series with the single-port SAWR when the transistor is in the OFF state and a closed switch that replaces the capacitance when the transistor is in the ON state to cause the first frequency F.sub.1 to be generated by the oscillator when the transistor is ON and to cause a second frequency. F.sub.2 to be generated by the oscillator when the transistor is in the OFF state.